6.a Inequalities

Question 1

What do you call this?

Answer 1

The real number line

Question 2

How would you draw, “x > 2” on the real number line?

Answer 2

Question 3

What does this line indicate?

Answer 3

Greater than 2

Question 4

What does this line indicate?

Answer 4

Greater than or EQUAL to 2

Question 5

When would the inequality sign flip?

Answer 5

When you DIVIDE or MULTIPLY by a NEGATIVE number

Question 6

Solve this:

Answer 6

The last line is divided by “-2”, so you flip the inequality sign

Question 7

Solve this:

Answer 7

Question 8

Can you add these inequalities? (if so, work it out)

Answer 8

Yes, because the signs are facing the same direction!

Question 9

Can you add these inequalities? (if so, work it out)

Answer 9

Yes, because the signs are facing the same direction!

Question 10

How would you solve this?

Answer 10

Question 11

How would you solve this?

Answer 11

WATCH OUT!!!!

Question 12

You can NOT multiply or divide an inequality where the ______________________

Answer 12

You can NOT multiply or divide an inequality where the VARIABLE is UNKNOWN

Question 13

What would you call this?

Answer 13

A compound inequality

Question 14

Solve this:

Answer 14

Dividing by a negative value, means the inequality signs will flip (REMEMBER)

Question 15

Solve this:

Answer 15

Question 16

Can you substitute from an equation into an inequality? (like the substitution rule)

Answer 16

YES!

Question 17

Solve this:

Answer 17

Question 18

Solve this:

Answer 18

Question 19

Draw this inequality on the number line

Answer 19

(GREATER THAN)

Question 20

Draw this inequality on the number line

Answer 20

Question 21

Solve this:

Answer 21

abs of -10 is still 10, dont forget!

Question 22

Solve and explain:

Answer 22

Question 23

If two absolute values are equal, it must be true that the expressions within the absolute values are either __________ or __________

Answer 23

If two absolute values are equal, it must be true that the expressions within the absolute values are either EQUAL or OPPOSITE

Question 24

How would you simplify absolute value inequalities?

Answer 24

Test two cases, one where the case is positive, one where the case is negative.

Question 25

What is an extraneous solution?

Answer 25

An answer that appears to be the solution but is NOT

Question 26

Solve and explain this:

Answer 26

Question 27

What is an efficient way to solve this?

Answer 27

You can just choose to test different values (eg. 0) to eliminate different answers!

Question 28

Solve this (the three solutions are 1, 3 and 5)

Answer 28

TEST THE VALUES!!!! 5 doesn't work, so its only 1 and 3

Question 29

What is super important in inequalities?

Answer 29

Once you have your solutions, TEST THEM!!!